--- title: The peak pattern puzzle keywords: fastai sidebar: home_sidebar summary: "Matching peak patterns " description: "Matching peak patterns " nb_path: "notebooks/40_peak-pattern-puzzle.ipynb" ---
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In the previous steps we have computed the hotmax spectra and within each spectrum detected peaks above the Poison noise level. All this preliminary work was needed to arrive at the central problem of MA-XRF analysis: solving the peak pattern puzzle. For each individual hotmax spectrum I would like to explain the presence of all peaks above the Poison noise level.

Before trying to assign peaks to the presence of specific elements in the scanned object, one should identify instrumental peaks that result from the physics of the instrument sensor or Rhodium anode.

{% raw %} 
from maxrf4u import HotmaxAtlas 

hma = HotmaxAtlas('RP-T-1898-A-3689.datastack')

hma.plot_spectra()
2022-05-13T10:43:49.492501 image/svg+xml Matplotlib v3.4.3, https://matplotlib.org/
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Or we can plot a single spectrum with HotmaxAtlas.plot_spectrum(<nr>)) to inspect a specific hotmax spectrum.

{% raw %} 
hma.plot_spectrum(4, headspace=3);
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Now we can start to 'explain away' all peaks...

To be continued...

{% raw %} 
hma = HotmaxAtlas('RP-T-1898-A-3689.datastack')
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fig, ax = plt.subplots(figsize=[9, 9])

n = 4 
ann_list = hma.plot_spectrum(n, ax=ax, headspace=2)

eoi_ptrns = get_patterns(eoi)

twax = ax.twinx()
plot_patterns(eoi_ptrns, ax=twax)
{% endraw %}

Module maxrf4u.peakpuzzle.py

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get_patterns[source]

get_patterns(elements, tube_keV=22)

Returns sorted pattern dict list, according to alpha peak energy.
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colorize[source]

colorize(elem=None, eoi=None)

Pick fixed color from nice color map for elements of interest.
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plot_patterns[source]

plot_patterns(ptrn_list, ax=None)

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len(eoi)

31
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get_patterns(['Fe'])

[{'elem': 'Fe',
  'name': 'Iron',
  'peaks_xy': array([[6.3941971 , 1.        ],
         [7.05452726, 0.13507831],
         [0.70435218, 0.02822656]]),
  'color': array([0.9, 0.1, 0.1])}]
{% endraw %} {% raw %} 
ptrn_list = get_patterns(eoi)
{% endraw %}

Let's plot these patterns

{% raw %} 
ptrn_list = get_patterns(eoi)
plot_patterns(ptrn_list)
{% endraw %} {% raw %} 
ptrn_list

[{'elem': 'N',
  'peaks_xy': array([[0.3961981, 1.       ]]),
  'color': [0.6196078431372549, 0.8549019607843137, 0.8980392156862745]},
 {'elem': 'O',
  'peaks_xy': array([[0.52826413, 1.        ]]),
  'color': [0.09019607843137255, 0.7450980392156863, 0.8117647058823529]},
 {'elem': 'F',
  'peaks_xy': array([[0.67133567, 1.        ]]),
  'color': [0.8588235294117647, 0.8588235294117647, 0.5529411764705883]},
 {'elem': 'Na',
  'peaks_xy': array([[1.04552276, 1.        ]]),
  'color': [0.7372549019607844, 0.7411764705882353, 0.13333333333333333]},
 {'elem': 'Mg',
  'peaks_xy': array([[1.25462731, 1.        ]]),
  'color': [0.7803921568627451, 0.7803921568627451, 0.7803921568627451]},
 {'elem': 'Al',
  'peaks_xy': array([[1.48574287, 1.        ]]),
  'color': [0.4980392156862745, 0.4980392156862745, 0.4980392156862745]},
 {'elem': 'Si',
  'peaks_xy': array([[1.73886943, 1.        ]]),
  'color': [0.9686274509803922, 0.7137254901960784, 0.8235294117647058]},
 {'elem': 'P',
  'peaks_xy': array([[2.014007, 1.      ]]),
  'color': [0.8901960784313725, 0.4666666666666667, 0.7607843137254902]},
 {'elem': 'S',
  'peaks_xy': array([[2.31115558, 1.        ]]),
  'color': [1.0, 0.9, 0.1]},
 {'elem': 'Cl',
  'peaks_xy': array([[2.61930965, 1.        ]]),
  'color': [0.5490196078431373, 0.33725490196078434, 0.29411764705882354]},
 {'elem': 'Ag',
  'peaks_xy': array([[2.98249125, 1.        ],
         [2.64132066, 0.03711157]]),
  'color': [0.8617627896065553, 0.8617627896065553, 0.8617627896065553]},
 {'elem': 'Cd',
  'peaks_xy': array([[3.13656828, 1.        ],
         [3.33466733, 0.54499009],
         [3.95097549, 0.04265699],
         [2.77338669, 0.03710945]]),
  'color': [0.6582003733660282, 0.6582003733660282, 0.6582003733660282]},
 {'elem': 'K',
  'peaks_xy': array([[3.31265633, 1.        ],
         [3.5877939 , 0.11613478]]),
  'color': [0.7725490196078432, 0.6901960784313725, 0.8352941176470589]},
 {'elem': 'Sn',
  'peaks_xy': array([[3.44472236, 1.        ],
         [3.68684342, 0.86217419],
         [4.3801901 , 0.08792298],
         [4.12706353, 0.06867461],
         [3.04852426, 0.03736927]]),
  'color': [0.9810565997395585, 0.8168056337199403, 0.8900357854757446]},
 {'elem': 'Ca',
  'peaks_xy': array([[3.68684342, 1.        ],
         [4.0170085 , 0.12565047]]),
  'color': [0.5803921568627451, 0.403921568627451, 0.7411764705882353]},
 {'elem': 'I',
  'peaks_xy': array([[3.93996998, 1.        ],
         [4.24812406, 0.834673  ],
         [5.07353677, 0.08740968],
         [4.7983992 , 0.08131471],
         [3.48874437, 0.03792133]]),
  'color': [0.9325913996040441, 0.6330005226112336, 0.8487053301493133]},
 {'elem': 'Ba',
  'peaks_xy': array([[4.46823412, 1.        ],
         [4.84242121, 0.8065798 ],
         [5.16158079, 0.16520084],
         [5.53576788, 0.09280552],
         [5.81090545, 0.0831585 ],
         [3.95097549, 0.03860967]]),
  'color': [0.8539442814235829, 0.7446473541924543, 0.721494327539966]},
 {'elem': 'Ti',
  'peaks_xy': array([[4.51225613, 1.        ],
         [4.93046523, 0.13026382],
         [0.44022011, 0.01364528]]),
  'color': [1.0, 0.596078431372549, 0.5882352941176471]},
 {'elem': 'V',
  'peaks_xy': array([[4.95247624, 1.        ],
         [5.42571286, 0.13198924],
         [0.50625313, 0.01739971]]),
  'color': [0.8392156862745098, 0.15294117647058825, 0.1568627450980392]},
 {'elem': 'Cr',
  'peaks_xy': array([[5.41470735, 1.        ],
         [5.94297149, 0.12885503],
         [0.57228614, 0.02085085]]),
  'color': [0.596078431372549, 0.8745098039215686, 0.5411764705882353]},
 {'elem': 'Mn',
  'peaks_xy': array([[5.89894947, 1.        ],
         [6.49324662, 0.13436239],
         [0.63831916, 0.02319039]]),
  'color': [0.17254901960784313, 0.6274509803921569, 0.17254901960784313]},
 {'elem': 'Fe',
  'peaks_xy': array([[6.3941971 , 1.        ],
         [7.05452726, 0.13507831],
         [0.70435218, 0.02822656]]),
  'color': [0.9, 0.1, 0.1]},
 {'elem': 'Co',
  'peaks_xy': array([[6.92246123, 1.        ],
         [7.64882441, 0.13586803],
         [0.7813907 , 0.03067365]]),
  'color': [1.0, 0.4980392156862745, 0.054901960784313725]},
 {'elem': 'Ni',
  'peaks_xy': array([[7.47273637, 1.        ],
         [8.26513257, 0.13651501],
         [0.85842921, 0.03262745]]),
  'color': [0.6823529411764706, 0.7803921568627451, 0.9098039215686274]},
 {'elem': 'Cu',
  'peaks_xy': array([[8.04502251, 1.        ],
         [8.90345173, 0.13519763],
         [0.93546773, 0.03435044]]),
  'color': [0.1, 0.9, 0.3]},
 {'elem': 'Zn',
  'peaks_xy': array([[8.62831416, 1.        ],
         [9.57478739, 0.13855054],
         [1.02351176, 0.03552537]]),
  'color': [0.7503608106413998, 0.9102271552918426, 0.9375127465007698]},
 {'elem': 'Hg',
  'peaks_xy': array([[ 9.981991  ,  1.        ],
         [11.84192096,  0.72592091],
         [ 2.22311156,  0.22576894],
         [13.83391696,  0.12703671],
         [ 8.72736368,  0.0539311 ],
         [14.20810405,  0.03217489],
         [ 1.71685843,  0.0255982 ],
         [10.64232116,  0.01723941]]),
  'color': [0.697834944396196, 0.5209247146284669, 0.47985790076901175]},
 {'elem': 'As',
  'peaks_xy': array([[10.53226613,  1.        ],
         [11.72086043,  0.15092996],
         [ 1.28764382,  0.04239893]]),
  'color': [0.23610902801167039, 0.8381621642481365, 0.882384963950054]},
 {'elem': 'Pb',
  'peaks_xy': array([[10.54327164,  1.        ],
         [12.61230615,  0.86061392],
         [ 2.37718859,  0.22474819],
         [14.76938469,  0.13372169],
         [ 9.1895948 ,  0.0562375 ],
         [12.30415208,  0.04622662],
         [15.17658829,  0.03288477],
         [ 1.82691346,  0.02578214],
         [11.34667334,  0.01782932]]),
  'color': [0.2, 0.2, 0.2]},
 {'elem': 'Br',
  'peaks_xy': array([[11.90795398,  1.        ],
         [13.29464732,  0.15988785],
         [ 1.49674837,  0.04610553]]),
  'color': [0.9127300741924363, 0.9127300741924363, 0.7008214073084114]},
 {'elem': 'Sr',
  'peaks_xy': array([[14.14207104,  1.        ],
         [15.83691846,  0.17388333],
         [ 1.82691346,  0.05557395]]),
  'color': [0.8328573088421117, 0.8355125433615939, 0.298512995129362]}]
{% endraw %} {% raw %} 
def get_instrument_patterns(datastack_file, anode='Rh', prominence=0.35): 
    '''Create instrument peak pattern dictionaries for sensor peak and Compton and elastic anode peaks.'''
    
    ds = maxrf4u.DataStack(datastack_file)
    
    # read max spectrum 
    ds = maxrf4u.DataStack(datastack_file)
    x_keVs = ds.read(ds.MAXRF_ENERGIES)
    y_max = ds.read(ds.MAXRF_MAXSPECTRUM)

    # locate peaks in max spectrum 
    peak_indices, _ = ssg.find_peaks(y_max, prominence=prominence)
    peaks_x = x_keVs[peak_indices]
    
    # assumes first peak is (negative) sensor peak 
    sensor_keV = peaks[0] 
    
    sensor_ptrn = {'source': 'SENSOR', 
                   'peaks_xy': np.array([[sensor_keV, 1]])}
    
    # anode peak pattern (including Compton)
    rhodium_peaks_x = mos.XFluo('Rh', tube_keV=40).peak_energies 
    Rh
    
    
    #anode_ptrn = 
     
    return peaks_x
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datastack_file = 'RP-T-1898-A-3689.datastack'
{% endraw %} {% raw %} 
ds = maxrf4u.DataStack(datastack_file)

y_sum = ds.read('maxrf_sumspectrum')
y_sum_without_sensor_peak = y_sum.copy()
y_sum_without_sensor_peak[x_keV < 1] = 0
Rh_Compton_i = np.argmax(y_sum_without_sensor_peak)
Rh_Compton_keV = x_keV[Rh_Compton_i]
Rh_Compton_keV
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rhodium_spectrum = mos.XFluo('Rh', tube_keV=40)
{% endraw %} {% raw %} 
rhodium_spectrum.peak_intensities

array([0.08118119, 1.        , 0.244193  , 0.04090913])
{% endraw %} {% raw %} 
rhodium_spectrum.peak_energies

array([ 2.70135068, 20.21010505, 22.71135568, 23.17158579])
{% endraw %} {% raw %} 
maxrf4u.RHODIUM_Ka

20.210105052526263
{% endraw %} {% raw %} 
peaks_x = get_instrument_patterns('RP-T-1898-A-3689.datastack')
peaks_x

array([-0.02864804,  0.53326082,  2.37953279,  2.62035087,  3.30266878,
        3.68396408,  4.00505485,  4.50675919,  4.84791815,  5.89146317,
        6.4032016 ,  7.06545133,  8.04879184,  8.65083705,  8.89165513,
        9.22277999, 10.55731354, 11.67109718, 12.6444036 , 14.46057331,
       14.80173226, 18.84546925, 20.21010505, 21.012832  ])
{% endraw %}

Let's plot these patterns...

{% raw %} 
eoi

array(['N', 'O', 'F', 'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'K', 'Ca',
       'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn', 'As', 'Br',
       'Sr', 'Ag', 'Cd', 'Sn', 'I', 'Ba', 'Hg', 'Pb'], dtype='<U3')
{% endraw %}

First we need to add the ANODE and SENSOR patterns.

{% raw %} 
ptrn_list

[{'elem': 'N', 'peaks_xy': array([[0.3961981, 1.       ]])},
 {'elem': 'O', 'peaks_xy': array([[0.52826413, 1.        ]])},
 {'elem': 'F', 'peaks_xy': array([[0.67133567, 1.        ]])},
 {'elem': 'Na', 'peaks_xy': array([[1.04552276, 1.        ]])},
 {'elem': 'Mg', 'peaks_xy': array([[1.25462731, 1.        ]])},
 {'elem': 'Al', 'peaks_xy': array([[1.48574287, 1.        ]])},
 {'elem': 'Si', 'peaks_xy': array([[1.73886943, 1.        ]])},
 {'elem': 'P', 'peaks_xy': array([[2.014007, 1.      ]])},
 {'elem': 'S', 'peaks_xy': array([[2.31115558, 1.        ]])},
 {'elem': 'Cl', 'peaks_xy': array([[2.61930965, 1.        ]])},
 {'elem': 'Ag',
  'peaks_xy': array([[2.98249125, 1.        ],
         [2.64132066, 0.03711157]])},
 {'elem': 'Cd',
  'peaks_xy': array([[3.13656828, 1.        ],
         [3.33466733, 0.54499009],
         [3.95097549, 0.04265699],
         [2.77338669, 0.03710945]])},
 {'elem': 'K',
  'peaks_xy': array([[3.31265633, 1.        ],
         [3.5877939 , 0.11613478]])},
 {'elem': 'Sn',
  'peaks_xy': array([[3.44472236, 1.        ],
         [3.68684342, 0.86217419],
         [4.3801901 , 0.08792298],
         [4.12706353, 0.06867461],
         [3.04852426, 0.03736927]])},
 {'elem': 'Ca',
  'peaks_xy': array([[3.68684342, 1.        ],
         [4.0170085 , 0.12565047]])},
 {'elem': 'I',
  'peaks_xy': array([[3.93996998, 1.        ],
         [4.24812406, 0.834673  ],
         [5.07353677, 0.08740968],
         [4.7983992 , 0.08131471],
         [3.48874437, 0.03792133]])},
 {'elem': 'Ba',
  'peaks_xy': array([[4.46823412, 1.        ],
         [4.84242121, 0.8065798 ],
         [5.16158079, 0.16520084],
         [5.53576788, 0.09280552],
         [5.81090545, 0.0831585 ],
         [3.95097549, 0.03860967]])},
 {'elem': 'Ti',
  'peaks_xy': array([[4.51225613, 1.        ],
         [4.93046523, 0.13026382],
         [0.44022011, 0.01364528]])},
 {'elem': 'V',
  'peaks_xy': array([[4.95247624, 1.        ],
         [5.42571286, 0.13198924],
         [0.50625313, 0.01739971]])},
 {'elem': 'Cr',
  'peaks_xy': array([[5.41470735, 1.        ],
         [5.94297149, 0.12885503],
         [0.57228614, 0.02085085]])},
 {'elem': 'Mn',
  'peaks_xy': array([[5.89894947, 1.        ],
         [6.49324662, 0.13436239],
         [0.63831916, 0.02319039]])},
 {'elem': 'Fe',
  'peaks_xy': array([[6.3941971 , 1.        ],
         [7.05452726, 0.13507831],
         [0.70435218, 0.02822656]])},
 {'elem': 'Co',
  'peaks_xy': array([[6.92246123, 1.        ],
         [7.64882441, 0.13586803],
         [0.7813907 , 0.03067365]])},
 {'elem': 'Ni',
  'peaks_xy': array([[7.47273637, 1.        ],
         [8.26513257, 0.13651501],
         [0.85842921, 0.03262745]])},
 {'elem': 'Cu',
  'peaks_xy': array([[8.04502251, 1.        ],
         [8.90345173, 0.13519763],
         [0.93546773, 0.03435044]])},
 {'elem': 'Zn',
  'peaks_xy': array([[8.62831416, 1.        ],
         [9.57478739, 0.13855054],
         [1.02351176, 0.03552537]])},
 {'elem': 'Hg',
  'peaks_xy': array([[ 9.981991  ,  1.        ],
         [11.84192096,  0.72592091],
         [ 2.22311156,  0.22576894],
         [13.83391696,  0.12703671],
         [ 8.72736368,  0.0539311 ],
         [14.20810405,  0.03217489],
         [ 1.71685843,  0.0255982 ],
         [10.64232116,  0.01723941]])},
 {'elem': 'As',
  'peaks_xy': array([[10.53226613,  1.        ],
         [11.72086043,  0.15092996],
         [ 1.28764382,  0.04239893]])},
 {'elem': 'Pb',
  'peaks_xy': array([[10.54327164,  1.        ],
         [12.61230615,  0.86061392],
         [ 2.37718859,  0.22474819],
         [14.76938469,  0.13372169],
         [ 9.1895948 ,  0.0562375 ],
         [12.30415208,  0.04622662],
         [15.17658829,  0.03288477],
         [ 1.82691346,  0.02578214],
         [11.34667334,  0.01782932]])},
 {'elem': 'Br',
  'peaks_xy': array([[11.90795398,  1.        ],
         [13.29464732,  0.15988785],
         [ 1.49674837,  0.04610553]])},
 {'elem': 'Sr',
  'peaks_xy': array([[14.14207104,  1.        ],
         [15.83691846,  0.17388333],
         [ 1.82691346,  0.05557395]])}]
{% endraw %}

Then, we need to start matching the peak patterns.